逆奇异值问题的一个二阶收敛算法  

A QUADRATICALLY CONVERGENT ALGORITHM FOR INVERSE SINGULAR VALUE PROBLEMS

作　　者：魏水艳 陈小山[2] Wei Shuiyan;Chen Xiaoshan(Yongzhou Normal College,Yongzhou 425100 China;School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China)

机构地区：[1]永州师范高等专科学校,永州425100 [2]华南师范大学数学科学学院,广州510631

出　　处：《计算数学》2021年第4期471-483,共13页Mathematica Numerica Sinica

基　　金：国家自然科学基金面上项目(11771159);粤港澳应用数学中心项目(2020B1515310013)资助。

摘　　要：设n+1个m×n(m≥n)实矩阵{A_(i)}_((i=0))^(n)和给定的n个正数{σ_(i)^(*)}_((i=1))^(n).本文研究如下的逆奇异值问题:求n个实数{c_(i)^(*)}_((i=1))^(n),使得矩阵A_(0)+c_(1)^(*)A_(1)+…+c_(n)^(*)A_(n)有奇异值{σ_(i)^(*)}_((i=1))^(n).基于矩阵方程,我们给出了求解逆奇异值问题的一个新的算法,并证明了它的二阶收敛特性.该算法可以看成是Aishima[Linear Algebra and its Applications,2018,542:310-333]中逆对称特征值问题算法的推广.数值例子表明算法的有效性.Let {A_(i)}_((i=0))^(n) bereal matrices with size and givenpositive numbers {σ_(i)^(*)}_((i=1))^(n).The purpose of this paper is to study the following inverse singular value problems:findreal numbers {c_(i)^(*)}_((i=1))^(n) such that the singular values of the matrix A_(0)+c_(1)^(*)A_(1)+…+c_(n)^(*)A_(n) are {σ_(i)^(*)}_((i=1))^(n).Based on the matrix equations,we propose a new numerical algorithm and analyze that it is of quadratic convergence.The new algorithm can be considered as a generalization of inverse symmetric eigenvalue problems in[Aishima,Linear Algebra and its Applications,2018,542:310-333].Numerical experiments show that new algorithm is effective.

关 键 词：逆奇异值问题 矩阵方程 二阶收敛 

分 类 号：O151.21[理学—数学]